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This chapter introduces two implementations of the valley model for multifractal continuous-time random walks on amorphous substrates. The first implementation focuses on the Gaussian substrate (Sect. 8.2), while the second involves the stretched exponential amorphous substrate (Sects. 8.3 and 8.3.3). In both examples, we demonstrate that the (unconditional) q-moments of inter-event times, reliant on complex statistical frameworks, can be represented in a scale-invariant form governed by exponents that are nonlinear functions of the order q. In this chapter, we illustrate how to transition from a disordered exponential substrate that fails to exhibit multifractality to one that does.

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Valley Model of Multifractal Continuous-Time Random Wandering on Amorphous Substrates

  • 章节

  • 发表日期：

    2025年

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  • Michał Chorowski,
  • Tomasz Gubiec,
  • Ryszard Kutner

摘要

This chapter introduces two implementations of the valley model for multifractal continuous-time random walks on amorphous substrates. The first implementation focuses on the Gaussian substrate (Sect. 8.2), while the second involves the stretched exponential amorphous substrate (Sects. 8.3 and 8.3.3). In both examples, we demonstrate that the (unconditional) q-moments of inter-event times, reliant on complex statistical frameworks, can be represented in a scale-invariant form governed by exponents that are nonlinear functions of the order q. In this chapter, we illustrate how to transition from a disordered exponential substrate that fails to exhibit multifractality to one that does.